Answer to Question #101646 in Statistics and Probability for Josanpreet

Question

1. The reading speed of sixth grade students is approximately normal with a mean speed of 125 words per minute and standard deviation of 24 words per minute .
a) what is the probability that a randomly selected srudent will read more than 130 words per minute ?
b) What is the probability that the mean reading rate for a random sample of 12 sixth grade students is more than 130 words per minute ?

c) What is the probability that the mean reading rate for a random sample of 24 sixth grade students is more than 130 words per minute ?

Answer 1

Mean = 125 and standard deviation = 24

(a) Probability of student will read more than 130 words per minute:

z score for x = 130 is:

z = (130 - 125)/24 = 0.21

P(x > 130) = P(z > 0.21) = 1-0.5832 = 0.4168 (using standard normal table)

(b) When sample size n = 12,

standard error of mean = 24/ 12^0.5 = 6.928

z score = (130 - 125)/6.928 = 0.72

P(x > 130) = P(z > 0.72) = 1-0.7642 = 0.2358 (using standard normal table)

(c) When sample size n = 24,

standard error of mean = 24/ 24^0.5 = 4.899

z score = (130 - 125)/4.899 = 1.02

P(x > 130) = P(z > 1.02) = 1-0.8461= 0.1539 (using standard normal table)